Measurement of the Coulomb quadrupole amplitude in the * p (1232) - PowerPoint PPT Presentation

Measurement of the Coulomb quadrupole amplitude in the � * p � � (1232) reaction in the low momentum transfer region David Anez Dalhousie University April 20, 2010

Introduction � Take measurements of the p ( e , e � p ) � 0 (pion electroproduction) reaction � At energies in the area of the � resonance � With low momentum transfer ( Q 2 ) between the electron and proton � To better understand the Coulomb quadrupole transition amplitude behavior in this region and how it affects nucleon deformation David Anez – April 20 th , 2010 2/29

Overview � Motivation: Constituent Quark Model � Kinematics and Transition Amplitudes � Response Functions and Amplitude Extraction � World Data and Models � Experimental Setup � Conclusions David Anez – April 20 th , 2010 3/29

Motivation: Constituent Quark Model � Three “heavy” quarks in nucleon � Each quark has mass 1 ⁄ 3 of nucleon � Each quark has intrinsic spin angular momentum of 1 ⁄ 2 � Combines to give S = 1 ⁄ 2 or S = 3 ⁄ 2 � If L = 0 + � corresponds to N (939) � S = 1 ⁄ 2 , J � = 1 ⁄ 2 + � corresponds to � (1232) � S = 3 ⁄ 2 , J � = 3 ⁄ 2 � If L = 2 + � corresponds to � (1232) � S = 1 ⁄ 2 , J � = 3 ⁄ 2 � S = 3 ⁄ 2 , J � = 1 ⁄ 2 + � corresponds to N (939) David Anez – April 20 th , 2010 4/29

Motivation: Constituent Quark Model � Wave functions created ( ) ( ) ( ) + + π π = = 1 = = 1 + = 3 = = 1 N 939 a S , L 0 J a S , L 2 J � S 2 2 D 2 2 ( ) + ( ) + ( ) π π ∆ = = 3 = = 3 + = 1 = = 3 1232 b S , L 0 J b S , L 2 J � S 2 2 D 2 2 David Anez – April 20 th , 2010 5/29

Motivation: Constituent Quark Model � Measure non-spherical components by measuring quadrupole moment � Cannot measure quadrupole moment directly � Measure quadrupole moment of N � � transition � Three electromagnetic transitions � M 1 – magnetic dipole � E 2 – electric quadrupole � C 2 – Coulomb/scalar quadrupole David Anez – April 20 th , 2010 6/29

Motivation: Constituent Quark Model � Magnetic Dipole � Spin-flip � Dominant David Anez – April 20 th , 2010 7/29

Motivation: Constituent Quark Model � Electric quadrupole � Coulomb quadrupole � Only with virtual photons David Anez – April 20 th , 2010 8/29

Motivation: Constituent Quark Model � One-body interactions 3 π � 16 � � ( ) ( ) ˆ 2 2 2 2 � = = − Q e r Y r e 3 z r [ 1 ] i i 0 i i i i 5 = i 1 i � Two-body interactions 3 � � � ( ) ˆ = σ σ − σ ⋅ σ Q B e 3 � [ 2 ] i iz jz i j ≠ = i j 1 David Anez – April 20 th , 2010 9/29

Motivation: Constituent Quark Model � Pion Cloud David Anez – April 20 th , 2010 10/29

Kinematics – Electronic Vertex � Incoming electron � Energy E � � Momentum k i k i � Scattered electron � Energy E � � k � Momentum k f f � Angle � e � Virtual photon � Energy � � � Momentum q q � Angle � q David Anez – April 20 th , 2010 11/29

Kinematics – Electronic Vertex � Momentum transfer, Q 2 � 2 2 2 2 = − = − ω − Q q ( q ) � θ 2 2 ′ e ≈ Q 4 E E sin � 2 David Anez – April 20 th , 2010 12/29

Kinematics – Hadronic Vertex � Recoil proton � Energy E p � � Momentum p p p p � Angle � pq � Recoil pion � Energy E � � � Momentum p � p π � Angle � � � Not detected David Anez – April 20 th , 2010 13/29

Kinematics – Planes � � � Scattering plane – k i and k f k k i f � � � Recoil plane – p p and p � p p π p � Azimuthal angle – φ pq David Anez – April 20 th , 2010 14/29

Multipole Amplitudes � General form of � N Multipoles: I X ± � � X – type of excitation (M, E, S) � I – isospin of excited intermediate state � � ± – J � = � ± 1 ⁄ 2 3 / 2 � Magnetic dipole – M 1 / M 1 + 3 / 2 � Electric quadrupole – E 2 / E 1 + 3 / 2 � Coulomb quadrupole – C 2 / S 1 + � ω + = S q L � + 1 1 David Anez – April 20 th , 2010 15/29

Multipole Amplitudes � N -Multipoles � N -Multipoles Initial State Excited State Final State π N * I 2 I 2 J � C , E , M π π π L � ± , E � ± , M � ± L π s s I J γ π N N R 0 + 1 ⁄ 2 + 1 ⁄ 2 + 1 ⁄ 2 + 1 + C 0 P 11 P 31 L 1− C 1, E 1 1 − 1 ⁄ 2 + 1 ⁄ 2 − S 11 S 31 1 ⁄ 2 + 0 − L 0+ , E 0+ 1 ⁄ 2 + 3 ⁄ 2 − 1 ⁄ 2 + 2 − D 13 D 33 L 2− , E 2− M 1 1 + 1 ⁄ 2 + 1 ⁄ 2 + P 11 P 31 1 ⁄ 2 + 1 + M 1− 1 ⁄ 2 + 3 ⁄ 2 + 1 ⁄ 2 + 1 + P 13 P 33 M 1+ 2 + 1 ⁄ 2 + 3 ⁄ 2 + 1 ⁄ 2 + 1 + C 2, E 2 P 13 P 33 L 1+ , E 1+ 1 ⁄ 2 + 5 ⁄ 2 + F 15 F 35 1 ⁄ 2 + 3 + L 3− , E 3− 2 − 1 ⁄ 2 + 3 ⁄ 2 − 1 ⁄ 2 + 2 − M 2 D 13 D 33 M 2− 1 ⁄ 2 + 5 ⁄ 2 − D 15 D 35 1 ⁄ 2 + 2 − M 2+ David Anez – April 20 th , 2010 16/29

Multipole Amplitudes � E 1+ and S 1+ at same magnitude as background amplitudes � Measure ratio to dominant M 1+ ( ) � � 3 / 2 * E Re E M � � 3 / 2 + + + 1 1 1 = = R EM Re � � � EMR = 3 / 2 2 � � M M 1 + + 1 ( ) � � 3 / 2 * S Re S M � � 3 / 2 + + + 1 1 1 = = R CM Re � CMR = � � 3 / 2 2 � � M M 1 + + 1 David Anez – April 20 th , 2010 17/29

Response Functions � Unpolarized cross section made up of four independent partial cross sections 5 σ d k ( ) = Γ σ + σ + σ + σ γ L T LT TT * Ω Ω dk d d q f e 0 k k 2 2 2 2 α 1 + − W m m Q p − γ f π Γ = 2 ε S = ε = k m γ 2 2 π 2 π − ε 2 k Q 1 2 q 4 W i 2 − − 2 1 2 2 � + � − W m W m 2 θ q p � � p = = k 2 q e ε = 1 2 tan � � γ 0 2 2 m 2 W � � Q 2 p David Anez – April 20 th , 2010 18/29

Response Functions � Unpolarized cross section made up of four independent partial cross sections 5 σ d k ( ) = Γ σ + σ + σ + σ γ L T LT TT * Ω Ω dk d d q f e 0 * cos ( ) σ = ε R * σ = ε + ε θ φ 2 1 R sin L S L LT S LT pq pq 2 * * σ = R σ = ε θ φ R sin cos 2 T T TT TT pq pq David Anez – April 20 th , 2010 19/29

Response Functions 2 ( ) ω { } { } { } 2 2 2 2 � ( ) * * 2 * cm = + + − + θ + + θ + R L 4 L L 4 Re L L 2 cos Re L 4 L L 12 cos L Re L L L 0 + 1 + 1 − 1 + 1 − 0 + 1 + 1 − 1 + 1 + 1 − 2 Q { } � 2 2 2 ( ) * = + 1 + + 1 − + + θ + − R T E 2 M M 3 E M M 2 cos Re E 3 E M M 0 + 2 1 + 1 − 2 1 + 1 + 1 − 0 + 1 + 1 + 1 − ( ) 2 2 2 2 + θ + − − 1 + − 1 − − cos 3 E M M 2 M M 3 E M M 1 + 1 + 1 − 2 1 + 1 − 2 1 + 1 + 1 − 2 ω { ) ( ) ( ) } � ( ( ) * * * * * cm = − θ − + − − + θ − + + R sin Re L 3 E M M 2 L L E 6 cos L E M M L E LT 0 + 1 + 1 + 1 − 1 + 1 − 0 + 1 + 1 + 1 + 1 − 1 − 1 + 2 Q ( ) � { } 2 2 ( ) 2 * * = θ 3 − 1 − − + R TT 3 sin E M Re E M M M M 2 1 + 2 1 + 1 + 1 + 1 − 1 + 1 − David Anez – April 20 th , 2010 20/29

Response Functions � Truncated Multipole Expansion ≈ R 0 � L { } 2 2 * 2 ≈ 5 + θ − 3 θ R M 2 cos Re E M cos M � T 1 + 0 + 1 + 1 + 2 2 { } ( ) * * ≈ θ − θ sin Re 6 cos R L M L M � + + + + LT 0 1 1 1 ( ) { } 2 2 * * ≈ − θ 1 + + R 3 sin M Re E M M M � + + + + − TT 2 1 1 1 1 1 � Model Dependent Extraction � Fit theoretical model to existing data � Insert model values for background amplitudes David Anez – April 20 th , 2010 21/29

World Data and Models � p ( e , e � p ) � 0 experiments � Models � MAID � CEA – 1969 � SAID � DESY – 1970-1972 � DMT � NINA – 1971 � Sato-Lee � ELSA – 1997 � Chiral EFT � MIT-Bates – 2000 � Lattice QCD � MAMI – 2001 � CLAS – 2002 � MAMI – 2005-2006 David Anez – April 20 th , 2010 22/29

World Data and Models David Anez – April 20 th , 2010 23/29

World Data and Models David Anez – April 20 th , 2010 24/29

World Data and Models David Anez – April 20 th , 2010 24/29

World Data and Models � Q 2 = 0.040 (GeV/ c ) 2 � New lowest CMR value � � e = 12.5° David Anez – April 20 th , 2010 24/29

World Data and Models � Q 2 = 0.040 (GeV/ c ) 2 � New lowest CMR value � � e = 12.5° � Q 2 = 0.125 (GeV/ c ) 2 � Validate previous measurements David Anez – April 20 th , 2010 24/29

World Data and Models � Q 2 = 0.040 (GeV/ c ) 2 � New lowest CMR value � � e = 12.5° � Q 2 = 0.125 (GeV/ c ) 2 � Validate previous measurements � Q 2 = 0.090 (GeV/ c ) 2 � Bridge previous measurements David Anez – April 20 th , 2010 24/29